Between the cylinders is e 2 ke r v 2 ke ln ba the

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Unformatted text preview: d, the energy is stored as chemical energy in the battery • When the switch is closed, the energy is transformed from chemical to electric potential energy Capacitance of a Cylindrical Capacitor
• From Gauss’ Law, the field between the cylinders is E = 2 ke / r • V = -2 ke ln (b/a) • The capacitance becomes Circuit Symbols
• A circuit diagram is a simplified representation of an actual circuit • Circuit symbols are used to represent the various elements • Lines are used to represent wires • The battery’s positive terminal is indicated by the longer line Capacitors in Parallel
• When capacitors are first connected in the circuit, electrons are transferred from the left plates through the battery to the right plate, leaving the left plate positively charged and the right plate negatively charged Q = Q1 + Q2 V1 = V2 = Vbatt C=C1+C2 Capacitors in Parallel, 2
• The flow of charges ceases when the voltage across the capacitors equals that of the battery • The capacitors reach their maximum charge when the flow of charge ceases • The total charge is equal to the sum of the charges on the capacitors
– Q = Q1 + Q2 • The potential difference across the capacitors is the same
– And each is equal to the voltage of the battery Capacitors in Parallel, 3
• The capacitors can be replaced with one capacitor with a capacitance of Ceq
– The equivalent capacitor must have exactly the same external effect on the circuit as the original capacitors Capacitors in Series
• When a battery is connected to the circuit, electrons are transferred from the left plate of C1 to the right plate of C2 through the battery Capacitors in Series, 2
• As this negative charge accumulate...
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